The Earth's orientation is defined as the rotation beween a rotating geocentric set of axes linked to the Earth Gxyz (the terrestrial system materialized by the coordinates of observing stations) and a non-rotating geocentric set of axes linked to inertial space GXYZ (the celestial system materialized by coordinates of stars, quasars, objects of the solar system). The common way for describing the Earth rotation is to specify the rotation matrix between these two systems.

If the Earth was rotating uniformly around a fixed rotation axis (with respect to the Earth crust and the celestial system), the Earth rotation changes would be described through one parameter only : the rotation angle varying linearly with time, or the time scale which can be derived from this rotation angle (the universal time).

Actually the rotation axis is neither fixed with respect to the crust nor with respect to a celestial system, and the Earth's rotation rate undergoes slight variations. The changes of the Earth rotation vector are caused by the gravitational torque exerted by the Moon, Sun and planets, displacements of matter in different parts of the planet and other excitation mechanisms. The observed oscillations can be interpreted in terms of mantle elasticity, earth flattening, structure and properties of the core-mantle boundary, rheology of the core, underground water, oceanic variability, and atmospheric variability on time scales of weather or climate. The understanding of the coupling between the various layers of our planet is also a key aspect of the research on the Earth's rotation.

In principle the Earth's orientation can be described through three independant angles (for instance the Euler angles). However the classical monitoring of the Earth's rotation considers separately the motion of the rotation axis in the Earth and in space. For routine determination of the Earth orientation, five Earth Orientation Parameters (EOP) are generally assessed. Technically, they are the parameters which provide the rotation of the International Terrestrial Reference Frame (ITRF) to the International Celestial Reference Frame (ICRF) as a function of time.

These parameters are refered to the Celestial Ephemeris Pole (CEP), which is close to the rotation pole. Its motion in space is the precession-nutation motion. Pratically its motion is equivalent to that of the geographic pole (ITRF pole) for periods greater than 2 days. The spatial position of the CEP is well modeled at a 0.001" accuracy by the luni-solar (and to a less-extent the planetary) torque on the Earth equatorial bulge and small additional impacts of atmospheric and oceanic effects.

The Celestial pole
offsets(dPsi, dEps)

However a precession-nutation model (such a model is kept as a part of the IERS Conventions) cannot take into account the variable components due to atmospheric, oceanic, and earth internal processes. The actual departure of the motion with the model is observed by VLBI and LLR. The observed differences with respect to the conventional celestial pole position defined by the model are monitored and reported by the IERS thanks to two Celestial pole offsets (dPsi, dEps).

The CEP remains very close to the instantaneous rotation axis (offset under 0.02"), and therefore is appropriate for reckoning the rotation angle of the Earth in space. The Earth's rotation is no more considered uniform, but still used for the common life. Therefore the IERS does not provide the Earth rotation angle, but the associated time scale UT1, that is the time which is required for the rotation angle if the Earth would rotate uniformly at the mean rotation rate (360°/86164.09891s). The tables provided to the users report the offset with respect uniform time scale TAI and UTC : UT1 - TAI / UT1 - UTC. The excess of the rotation period with respect to the mean period is called excess of length of day (LOD).

After applying the precession-nutation matrix corrected by the celestial pole offsets and the rotation angle around the CEP, a residual rotation remains to get into the International Reference Frame. It is associated with the 2 small angles (x,y), which are the coordinates of the pole (x,-y) of the CEP, relative to the Gz axis of the International Terrestrial Reference Frame (the geographic pole axis). The coordinates of the pole undergoes variations mostly because of atmospheric and oceanic mass redistributions as seasonal time scale. The terrestrial coordinates of the CEP correspond to the circular celestial motions of Gz axis having period smaller than 2 days, in turn their variations range from several years to a few minutes except the retrograde diurnal band.

N.B.: The x-axis is in the direction of the IERS Reference Meridian (the Greenwich Meridian) ; the y-axis is in the direction 90 degrees Est longitude.

Actually the original definition of the CEP, based upon a conventional precession-nutation model, does not take account of diurnal and higher frequency variations in the Earth's orientation. The XXIVth General Assembly of the IAU, held in Manchester in August 2000, has extended the concept of CEP to that one of CIP.

excerpt of resolution B1. 7

"The XXIVth IAU General Assembly [...] recommends [...] that

1. the Celestial Intermediate Pole (CIP) be the pole, the motion of which is specified in the Geocentric Celestial Reference System (GCRS)[...] by motion of the Tisserand mean axis of the Earth with periods freater than two days.
[...]

3. that the motion of the CIP in the GCRS be realised by the IAU 2000 A model for precession and forced nutation for periods greatr than two days plus additional time-dependant corrections provided by the International Earth Rotation Service (IERS) through appropriate astro-geodetic observations

4. that the motion of the CIP in the International Terrestrial Reference System (ITRS) be provided by the IERS through appropriate astro-geodetic observations and models including high-frequency variations
[..]

6. that implementation of the CIP be on 1 January 2003"

The implementation of the CIP will not modify the deep nature of the EOP, only brings some new constraints :

-The celestial pole offsets will be refered to the new precession-nutation model of the IAU (instead of the IAU 1980 model)
-The celestial pole offsets do not contain any high-frequency variations (as it is already realised, but not stated)